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Picture reconstruction from projections in restricted range
Author(s) -
Louis A. K.,
Törnig W.
Publication year - 1980
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670020207
Subject(s) - extrapolation , mathematics , range (aeronautics) , sobolev space , space (punctuation) , order (exchange) , convergence (economics) , algorithm , mathematical analysis , computer science , materials science , finance , economics , composite material , economic growth , operating system
In order to reduce scanning time modern x ‐ray scanners provide projections only in a restricted range [0, ϕ] with ϕ < π. We consider the reconstruction of pictures from p + 1 complete projections in [0, ϕ]. An extrapolation procedure is given to achieve approximations g p of the data in the whole range. We show that the L 2 ‐error of the corresponding picture is of order p −α if the original belongs to the Sobolev space H o α . The validity of our error estimate is investigated by numerical experiments.